Chapter 11 - Introduction to the Design of Discrete Filters

Abstract

This chapter introduces the most important application of linear time-invariant systems: filtering. The design and realization of discrete filters brings together topics such as quantization error and its effect on the filters, optimization methods for filter design, and stabilization of unstable filters. In the discrete-time domain, there are two possible types of filters. The first is the result of rational approximation—these filters are called recursive or infinite-impulse response (IIR) filters. The other is the non-recursive or finite-impulse response (FIR) filters that result from a polynomial approximation. The implementation of discrete or digital filters is done by means of software or dedicated hardware. The discrete filter specifications can be in the frequency or in the time domain. The classical analog design methods can be used to design discrete filters by means of the bilinear transformation that maps the analog s-plane into the Z-plane. Considering continuous-to-discrete converters (CDCs) and discrete-to-continuous converters (DCCs) as simply samplers and reconstruction filters, it is possible to implement the filtering of band-limited analog signals using discrete filters. The chapter also discusses the significance of design of discrete filters, for instance, of passive and active elements, feedback and operational amplifiers, reactance functions, and frequency transformation in analog filtering.